Space of modular forms of level 675, weight 1, and Character 675.c

• Label: 675.1.c
• Level: $675$
• Weight: $1$
• Character orbit: 675.c
• Rep. character: $\chi_{675}(26,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $90$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	675.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(90\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(675, [\chi])\).

	Total	New	Old
Modular forms	22	4	18
Cusp forms	4	4	0
Eisenstein series	18	0	18

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q + 2 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(675, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
675.1.c.a	$675$	$1$	675.c	3.b	$2$	$1$	$1$	$0.337$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{4}-q^{7}+2q^{13}+q^{16}-q^{19}+\cdots\)
675.1.c.b	$675$	$1$	675.c	3.b	$2$	$1$	$1$	$0.337$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{4}+q^{7}-2q^{13}+q^{16}-q^{19}+\cdots\)
675.1.c.c	$675$	$1$	675.c	3.b	$2$	$2$	$2$	$0.337$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-15}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-iq^{8}-q^{16}-iq^{17}+q^{19}+\cdots\)